I have an undirected graph $G$, with edges $E$ and vertex $V$, how to group the edges into different sets, in which
- One edge can only belong in one set
- Every edge must be covered in one of the sets
- If I can "walk" from one edge to another, these two edges must be contained in a single set.
Take this for an example, I have the following edges $(A,B), (C,B), (D,B),(B,G), (E,F)$, then there are two sets, namely, $(A,B), (C,B), (D,B),(B,G)$ and $(E,F)$.
Edit: My hunch tells me that there is a standard algorithm (with a name) for this, what is it?